Channel State and Receiver State feedback for frequency-selective block fading channels

In a fading communication channel, it is often beneficial to feedback Channel State Information (CSI) and Receiver State Information (RSI) to the transmitter. The CSI generally refers to information about the channel condition available at the receiver, while the RSI in this work is defined as information about the receive's estimate of the message. The RSI can be used to improve reliability, e.g., through retransmission. This paper considers multi-carrier transmission through a doubly-selective Rayleigh fading channel, and studies the trade-off between the feedback of CSI and RSI under total feedback constraint. In particular, the CSI feedback specifies which groups of subchannels to activate with equal power, and the RSI feedback determines retransmissions of a codeword. The problem is how to allocate feedback bits between CSI and RSI in order to maximize the error probability exponent. It is found that the optimal tradeoff exhibits phase transitions which depends critically on the coherence time and the total amount of feedback. Specifically, the first feedback bits should be CSI up to a critical amount. Additional feedback bits, if available, should be allocated to RSI first, and then to both CSI and RSI. For the model considered, as the amount of feedback exceeds a certain threshold, additional RSI feedback is not beneficial unless CSI feedback increases accordingly.